Correction: Earlier versions of this article, including in Wednesday’s print editon of The Washington Post, misstated the name of the person who was accused in 1984 of tying up a 10-year-old girl he had just raped and covering her with debris. The person was Joe Anthony Barber.

A convicted rapist was arrested Tuesday and accused of fatally stabbing a woman on New Year’s Day nearly 30 years ago in Southeast Washington, according to law enforcement authorities.

The arrest was made with the help of DNA evidence, police said. They said evidence stored in the decades-old case was linked to the suspect, who was released from prison in 2004 after serving about 19 years for rape.

The suspect, Joe Anthony Barber, 55, had been living in Woodbridge, Va., police said. They said that Barber had no apparent connection to the victim, 43-year-old Rachel Cox, and that they think the attack was random.

Police would not say what items were tested to get a DNA sample, a procedure that was not available 29 years ago. Now, police agencies collect genetic samples from many convicts. They also routinely use new techniques to extract DNA from clothing, tissue samples and other evidence from long­unsolved cases and run it through databases in hopes of a match.

“The technology that is developing gives us a chance,” D.C. Assistant Police Chief Peter Newsham said. “If you’re a family member of one of these cases, we do not forget.”

Little could be learned about Cox, who authorities said was sexually assaulted and stabbed repeatedly inside her home in the 3300 block of Sixth Street SE.

Cox’s daughter, a 48-year-old Beltsville, Md., resident, said her family was stunned by news of the arrest in a case that they thought had been forgotten.

“Everyone is excited. Everyone is happy,” said the daughter, who asked that her name not be made public. She said she is afraid to have her identity made known until more details emerge about the killing and the man police arrested Tuesday.

“We’re extremely emotional about the whole thing,” the daughter said. “We’re just getting all this information today. It’s overwhelming.”

The Washington Post reported Cox’s killing in a short article that told of two slayings on Jan. 1, 1984. The other victim was a man who was shot, also in Southeast Washington. Cox was the year’s second homicide in the District.

In October 1984, Barber was accused of abducting a 10-year-old girl as she walked by a playground near the District’s Martin Luther King Jr. Elementary School, dragging her into the woods and raping her. Authorities said Barber bound the girl and covered her with debris. The school is a block from where Cox lived and a little more than a mile from where Barber lived at the time.

Barber pleaded guilty to the rape in 1985 and was sentenced to nine to 35 years in prison.

According to the Virginia State Police sex offense database, Barber worked at a fitness company that deals in exercise equipment. Company officials said he stopped working there after the company declared bankruptcy. The company later reopened under a different name.

Jennifer Jenkins contributed to this article.